Patent Document 1 (JP 2009-092419 A) discloses an optical device that can determine the central coordinates of a columnar body, such as a utility pole, or a columnar structure. This optical device has a telescope. In the telescope, a reticle is provided. On the reticle, a concentric scale having a plurality of circles or arcs is drawn around an optical axis. The purpose of use of the optical device is not particularly limited. For example, when the central coordinates of a columnar body are measured using this optical device, a circle having a diameter closest to the diameter of the columnar body (image) projected onto the reticle is first inscribed or substantially inscribed in the columnar body (image). Then, the distance from the optical device to the columnar body and the direction of the columnar body from the optical device are measured. Then, the central coordinates of the columnar body is determined using the measured distance and direction and known information (specifically, the machine coordinates (reference coordinates) of the optical device and the radius of the columnar body).
As described above, in order to determine the central coordinates of a columnar body using the optical device disclosed in Patent Document 1, both the right and left edges of the columnar body need to be projected onto the reticle. However, a telescope used in a common survey instrumentation (total station) has a very narrow angle of view (e.g., about 1 degree). Therefore, when the survey instrumentation is close to a columnar body, part of the columnar body is seen through an eyepiece lens (i.e., part of the columnar body is projected onto a reticle as an image), that is, it is difficult to allow both the right and left edges of the columnar body to be included in one image at the same time. For this reason, in order to allow a survey instrumentation or the like to satisfy the above requirement, a columnar body needs to have a quite small diameter, or the survey instrumentation needs to keep enough distance from a columnar body. However, when the central coordinates of a pile, which is a cylindrical structure that functions as a foundation for a building, are measured to determine the condition of the pile that is being driven (i.e., to determine whether or not the pile is being properly driven in a proper position), the survey instrumentation needs to keep a distance of about 30 meters or more from the pile, because the pile generally has an outer diameter of about 30 centimeters or more. However, at a construction site where buildings are concentrated, there are cases where the survey instrumentation cannot keep enough distance from a pile. Particularly, in recent years, a high-rise building is often constructed at a site where buildings are concentrated. In this case, it is substantially difficult to determine the central coordinates of a large-diameter pile whose diameter is larger than one meter.